Midpoint circle algorithm - Revision history

en>Ari Rahikkala: Remove a redundant 'only'

2014-12-27T05:40:50Z

Remove a redundant 'only'

← Older revision		Revision as of 07:40, 27 December 2014
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	~~Alyson Meagher~~ is the title ~~her parents gave her~~ but ~~she doesn~~'~~t like when individuals use her complete name~~. ~~To perform lacross is one~~ of ~~the issues she loves most~~. ~~Mississippi is where her home is but her husband wants them to transfer~~. He is ~~an order clerk and it's some thing~~ he ~~truly enjoy~~.<br><br>~~Feel free to~~ visit my ~~page~~: real ~~psychics~~ ([http://~~black7~~.~~mireene~~.com/~~aqw~~/~~5741 Recommended Web site~~])		Golda is what's written on my beginning certification although it is not the title on my birth certificate. I've always cherished living in Kentucky but now I'm contemplating other choices. I am really fond of handwriting but free tarot readings ([http://galab-work.cs.pusan.ac.kr/Sol09B/?document_srl=1489804 http://galab-work.cs.pusan.ac.kr/Sol09B/?document_srl=1489804]) I can't make it my occupation really. Distributing production is how he makes a residing.<br><br>Also visit my web-site: [http://www.familysurvivalgroup.com/easy-methods-planting-looking-backyard/ real psychic readings] solutions by lynne ([http://hknews.classicmall.com.hk/groups/some-simple-tips-for-personal-development-progress/ http://hknews.classicmall.com.hk/groups/some-simple-tips-for-personal-development-progress])

68.125.49.144: /* Algorithm */ still editing sketch

2014-02-23T21:36:05Z

Algorithm: still editing sketch

← Older revision		Revision as of 23:36, 23 February 2014
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	'~~''Kuratowski's free set theorem''', named after [[Kazimierz Kuratowski]],~~ is ~~a result~~ of ~~[[set theory]], an area of [[mathematics]]~~. It is ~~a result which has been largely forgotten for almost 50 years,~~ but ~~has been applied recently in solving several [[lattice theory]] problems, such as the [[Congruence Lattice Problem]]~~.		Alyson Meagher is the title her parents gave her but she doesn't like when individuals use her complete name. To perform lacross is one of the issues she loves most. Mississippi is where her home is but her husband wants them to transfer. He is an order clerk and it's some thing he truly enjoy.<br><br>Feel free to visit my page: real psychics ([http://black7.mireene.com/aqw/5741 Recommended Web site])

	Denote by <math>[X]^{<\omega}</math> the [[Set (mathematics)\|set]] of all [[Finite set\|finite subsets]] of a set <math>X</math>. Likewise, for a [[positive integer]] <math>n</math>, denote by <math>[X]^n</math> the set of all <math>n</math>-elements subsets of <math>X</math>. ~~For a [[Map (mathematics)\|mapping]]~~ <~~math~~>~~\Phi\colon[X]^n\to[X]^{<\omega}~~<~~/math~~>~~, we say that a [[subset]] <math>U</math> of <math>X</math> is ''~~free~~'' (with respect~~ to ~~<math>\Phi</math>), if <math>u\notin\Phi~~(~~V)<~~/~~math>, for any <math>n<~~/~~math>-element subset <math>V</math> of <math>U</math> and any <math>u\in U\setminus V</math>~~. ~~[[Kuratowski]] published in 1951 the following result, which characterizes the [[Infinity\|infinite]] [[Cardinal number\|cardinals]] of the form <math>\aleph_n</math>~~.

	~~The theorem states the following. Let <math>n</math> be a positive integer and let <math>X</math> be a set. Then the [[cardinality]] of <math>X</math> is greater than or equal to <math>\aleph_n<~~/~~math> if and only if for every mapping <math>\Phi</math> from <math>[X]^n<~~/~~math> to <math>[X~~]~~^{<\omega}</math>,~~
	~~there exists an <math>(n+1~~)~~</math>-element free subset of <math>X</math> with respect to <math>\Phi</math>.~~

	~~For <math>n=1</math>, Kuratowski's free set theorem is superseded by [[Hajnal's set mapping theorem]].~~

	~~== References ==~~
	* [[Paul Erdős\|P. Erdős]], [[András Hajnal\|A. Hajnal]], A. Máté, [[Richard Rado\|R. Rado]]: ''Combinatorial Set Theory: Partition Relations for Cardinals'', North-Holland, 1984, pp. 282-285.
	* [[Kazimierz Kuratowski\|C. Kuratowski]], ''Sur une caractérisation des alephs'', Fund. Math. '''38''' (1951), 14--17.
	* John C. Simms: Sierpiński's theorem, ''Simon Stevin'', '''65''' (1991) 69--163.

	~~{{settheory-stub}}~~
	~~[[Category:Set theory]]~~

en>XxEmoKittenxx: /* Algorithm */

2014-01-26T18:18:24Z

Algorithm

← Older revision		Revision as of 20:18, 26 January 2014
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	~~Alyson~~ is the ~~name people use~~ to ~~contact me and I believe it sounds fairly good when you~~ say ~~it. Mississippi~~ is ~~the only place I~~'~~ve been residing in but I will have~~ to ~~move~~ in ~~a yr or two~~. ~~Invoicing is my occupation~~. The ~~favorite pastime for him~~ and ~~his children~~ is ~~style~~ and ~~he'll be beginning some thing else along~~ with it.<br><br>~~My web site;~~ [~~http~~:~~//chorokdeul~~.co.~~kr/index~~.~~php?document_srl=324263~~&~~mid=customer21 best psychics~~]		'''Kuratowski's free set theorem''', named after [[Kazimierz Kuratowski]], is a result of [[set theory]], an area of [[mathematics]]. It is a result which has been largely forgotten for almost 50 years, but has been applied recently in solving several [[lattice theory]] problems, such as the [[Congruence Lattice Problem]].

			Denote by <math>[X]^{<\omega}</math> the [[Set (mathematics)\|set]] of all [[Finite set\|finite subsets]] of a set <math>X</math>. Likewise, for a [[positive integer]] <math>n</math>, denote by <math>[X]^n</math> the set of all <math>n</math>-elements subsets of <math>X</math>. For a [[Map (mathematics)\|mapping]] <math>\Phi\colon[X]^n\to[X]^{<\omega}</math>, we say that a [[subset]] <math>U</math> of <math>X</math> is ''free'' (with respect to <math>\Phi</math>), if <math>u\notin\Phi(V)</math>, for any <math>n</math>-element subset <math>V</math> of <math>U</math> and any <math>u\in U\setminus V</math>. [[Kuratowski]] published in 1951 the following result, which characterizes the [[Infinity\|infinite]] [[Cardinal number\|cardinals]] of the form <math>\aleph_n</math>.

			The theorem states the following. Let <math>n</math> be a positive integer and let <math>X</math> be a set. Then the [[cardinality]] of <math>X</math> is greater than or equal to <math>\aleph_n</math> if and only if for every mapping <math>\Phi</math> from <math>[X]^n</math> to <math>[X]^{<\omega}</math>,
			there exists an <math>(n+1)</math>-element free subset of <math>X</math> with respect to <math>\Phi</math>.

			For <math>n=1</math>, Kuratowski's free set theorem is superseded by [[Hajnal's set mapping theorem]].

			== References ==
			* [[Paul Erdős\|P. Erdős]], [[András Hajnal\|A. Hajnal]], A. Máté, [[Richard Rado\|R. Rado]]: ''Combinatorial Set Theory: Partition Relations for Cardinals'', North-Holland, 1984, pp. 282-285.
			* [[Kazimierz Kuratowski\|C. Kuratowski]], ''Sur une caractérisation des alephs'', Fund. Math. '''38''' (1951), 14--17.
			* John C. Simms: Sierpiński's theorem, ''Simon Stevin'', '''65''' (1991) 69--163.

			{{settheory-stub}}
			[[Category:Set theory]]

115.247.140.92: /* Optimization */

2012-07-27T18:57:09Z

Optimization

New page

Alyson is the name people use to contact me and I believe it sounds fairly good when you say it. Mississippi is the only place I've been residing in but I will have to move in a yr or two. Invoicing is my occupation. The favorite pastime for him and his children is style and he'll be beginning some thing else along with it.<br><br>My web site; [http://chorokdeul.co.kr/index.php?document_srl=324263&mid=customer21 best psychics]